Convergence des solutions faibles du système de Vlasov-Maxwell stationnaire vers des solutions faibles du système de Vlasov-Poisson stationnaire quand la vitesse de la lumière tend vers l'infini

We study here the behavior of weak solutions for the relativistic stationary Vlasov-Maxwell system with boundary conditions in a three-dimensional bounded domain with strictly star-shaped boundary, when the light speed becomes infinite. We prove the convergence toward a weak solution for the stationary Vlasov-Poisson system. The time periodic problem and the problem with initial-boundary conditions can be treated by the same method. To cite this article: M. Bostan, C. R. Acad. Sci. Paris, Ser. I 340 (2005).